edfas.org 29 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 3 For high-temperature electronics and sensors, the temperature range to which the devices are exposed to is much wider compared with that for conventional electronics.[8] The most common failure mode of wire bonds is delamination/cracking at wire/bond-pad and bond- pad/chip (or substrate) interfaces. The failure of wire bonds may cause open and shorted circuits. The performance of these structures also depends on the design; they may be more sensitive to random variations in material and load uncertainties. Hence, the objective of this work is to develop a reliability-based design and optimization (RBDO) methodology to improve the performance and reliability of power devices. All relevant uncertainties influencing the probability of failure are then introduced in the vector X, where X consists of two kinds of variables: 1. Design variables Xd: These variables are deterministic and represent the control parameters of the mechanical system (e.g., dimensions, materials, loads) and of the probabilistic model (e.g., mean values and standard deviations of random variables).[17-21] 2. Random variables Xr: These variables can be geometrical dimensions, material characteristics or applied external loading. The uncertainties of each variable are modeled by statistical information.[9-16] The failure of the system is modeled by a functional relation G(X), called the limit state function. This function can either be implicit (e.g., the outcome of a numerical FEM code), or explicit (e.g., an approximate equation obtained using the response surface method). The limit between the state of failure G(X) < 0 and the state of safety G(X) > 0 is known as the limit state surface G(X) = 0. Given this formulation, the reliability design optimization problem of the wire bonding interconnection can be written as: Find Xd = [xd1, xd2, …, xdn] and Xr = [xr1, xr2, …, xrn] Such that to minimize Pf = Pf [G(Xd, Xr) ≤ 0] Subjected to cos t (Xd) ≤ C0,…Xlb ≤ X ≤ Xub (Eq 1) where C0 is the allowable cost, which is a function of a vector of design variable Xd, and Pf is the probability operator and failure probability corresponding to the performance function G. In this problem, the designer is to find the design, Xd that minimizes the probability of system failure of wire bonding under the cost constraint corresponding to the structural volume. FINITE ELEMENT ANALYSIS The Au wire is wedge bonded on two identical Au thickfilm bond pads on an alumina substrate (see Fig. 2). The length of both wedge bonds is 100 μm. The thickness of the substrate is 625 μm, and the substrate length is 10 times the distance between two wire bonds (from heel to heel). The Au wire is assumed to be composed of a flat bonded section (100 μm). The geometry of the wire and bonds is described using the seven variables shown in Table 1. To avoid tedious calculation and expensive computing resources, a two-dimensional analysis is performed in this study. The finite element mesh, the dimensions and boundary conditions of the numerical model are shown in Fig. 2. The symmetrical boundary conditions were applied along the left edge of the model. The left bottom corner was constrained in the vertical direction to prevent body Fig. 2 Finite element meshes, dimensions, and boundary conditions for the numerical model. Table 1 Initial design variables of the wire and bonds Description and units Initial design variables Y_WIRE, μm 25 Y_PAD, μm 25 c, μm 250 d, μm 250 ALPHA 30° e, μm 1375 r, μm 1250
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